p1spring08_l - Math 2930 Spring 08 Prelim 1 1. Given the...

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Unformatted text preview: Math 2930 Spring 08 Prelim 1 1. Given the following differential equation dy dx = 4 x- 2 y, y (0) = 0 (1) (a) Use Eulers method to approximate the differential equation on the interval x = [0 , 2]. Use a step size of h = 1 / 2 and clearly state any equations used. (b) Solve the differential equation dy dx = 4 x- 2 y , y (0) = 0. (c) What is the error is Eulers method for y (2) in part (a)? 2. The population of a duck pond is governed by the following differential equation dP dt = 2 P (4- P ) , P (0) = 2 (2) (a) Solve for the population as a function of time, P ( t ). (b) What is the limiting population? 3. Find the general solution to the differential equation dy dx = x + 2 y y- 2 x (3) For what initial conditions (if any) is the solution guaranteed to exist and be unique? 4. Given the differential equation below, answer the questions. dy dx = ( y- 1)(2- y )( y- r ) (4) (a) Calculate, then draw the bifurcation diagram for the system....
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p1spring08_l - Math 2930 Spring 08 Prelim 1 1. Given the...

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